https://catalog.csun.edu/academics/chem/programs/bs-biochemistry/ indicates that you need 52 upper division units for the biochemistry major. If you are missing 3 lower division courses, then you need 9-14 lower division units (depending on which ones), so that makes up 61-66 total units you need for your major. Upper division GE not covered by your major is another 6 units, according to https://catalog.csun.edu/general-education/upper-division/ . That leaves you -2 to 3 units within the 140 unit cap if you transfer in with 70 units. The 3-5 extra courses you want to take presumably will be from 9-20 units, but check if any can count as upper division GE.
Perhaps find out if the unit cap applies only after crossing 140 units, versus applying as you approach 140 units. If it applies only after crossing 140 units, you could finish a semester with 139 units and then take another 15 or so units in your last semester before graduation. But if it applies as you approach 140 units, then that may not be possible.